交大OCW 江蕙如演算法投影片 https://www.youtube.com/watch?v=7a28lIQIHJQ&list=PLj6E8qlqmkFtoRpLn6IXnH_eboef-3QvZ&index=1

1. Iris Hui-Ru Jiang Fall 2014
DEE3504
ALGORITHMS
IRIS H.-R. JIANG
Administrative Matters
Introduction
2
¨ Time/location: 1CD3A@SC204
¨ Instructor: 㱆啀⥩ Iris Hui-Ru Jiang
¤ Email: huiru.jiang@gmail.com
¤ Office: ED540, ext. 31211
¤ Office hours: 1X (made by appointment)
¨ Teaching assistants: 愔⭰ⓙ㜵㉦䝦
¤ Email: nctuee.alg@gmail.com
¤ Lab: ED413, ext. 54226
¤ Office hours: 2EF
¨ Prerequisite: two out of the following courses
¤ Data structures
¤ Discrete mathematics
¤ Computer programming in C
¤ Computer programming in C++
IRIS H.-R. JIANG
Reading Materials
Introduction
3
¨ Course webpage:
¤ e3, NCTU open course ware
¨ Required text:
¤ Kleinberg and Tardos, Algorithm Design, Addison Wesley, 2006
n Jon Kleinberg, 20 Best Brains under 40, Discover Magazine,
2008
n Cornell
¨ Reference:
¤ S. Dasgupta, C. H. Papadimitriou, and U. V. Vazirani, Algorithms,
McGraw-Hill, 2007
n UC Berkeley
¤ Cormen, Leiserson, Rivest, Stein, Introduction to Algorithms, 3rd
Ed., McGraw Hill/MIT Press, 2009
n Bible! MIT
IRIS H.-R. JIANG
Course Objectives
Introduction
4
¨ Study unifying principles and concepts of algorithm design
¤ Algorithmic problems form the heart of computer science
¨ Polish your critical thinking and problem-solving technique
¤ Algorithmic problems tend to come bundled together with lots of
messy, application-specific detail, some of it essential, some of it
extraneous
¤ Two fundamental components
n Get to the mathematically clean core of a problem
n Identify the appropriate algorithm design techniques based on
the structure of the problem
¨ Intended audience:
¤ Who are interested in computer science
¤ Who are computing something
¤ Who are learning problem-solving techniques

2. Iris Hui-Ru Jiang Fall 2014
DEE3504
ALGORITHMS
IRIS H.-R. JIANG
Administrative Matters
Introduction
2
¨ Time/location: 1CD3A@SC204
¨ Instructor: 㱆啀⥩ Iris Hui-Ru Jiang
¤ Email: huiru.jiang@gmail.com
¤ Office: ED540, ext. 31211
¤ Office hours: 1X (made by appointment)
¨ Teaching assistants: 愔⭰ⓙ㜵㉦䝦
¤ Email: nctuee.alg@gmail.com
¤ Lab: ED413, ext. 54226
¤ Office hours: 2EF
¨ Prerequisite: two out of the following courses
¤ Data structures
¤ Discrete mathematics
¤ Computer programming in C
¤ Computer programming in C++
IRIS H.-R. JIANG
Reading Materials
Introduction
3
¨ Course webpage:
¤ e3, NCTU open course ware
¨ Required text:
¤ Kleinberg and Tardos, Algorithm Design, Addison Wesley, 2006
n Jon Kleinberg, 20 Best Brains under 40, Discover Magazine,
2008
n Cornell
¨ Reference:
¤ S. Dasgupta, C. H. Papadimitriou, and U. V. Vazirani, Algorithms,
McGraw-Hill, 2007
n UC Berkeley
¤ Cormen, Leiserson, Rivest, Stein, Introduction to Algorithms, 3rd
Ed., McGraw Hill/MIT Press, 2009
n Bible! MIT
IRIS H.-R. JIANG
Course Objectives
Introduction
4
¨ Study unifying principles and concepts of algorithm design
¤ Algorithmic problems form the heart of computer science
¨ Polish your critical thinking and problem-solving technique
¤ Algorithmic problems tend to come bundled together with lots of
messy, application-specific detail, some of it essential, some of it
extraneous
¤ Two fundamental components
n Get to the mathematically clean core of a problem
n Identify the appropriate algorithm design techniques based on
the structure of the problem
¨ Intended audience:
¤ Who are interested in computer science
¤ Who are computing something
¤ Who are learning problem-solving techniques

3. Iris Hui-Ru Jiang Fall 2014
DEE3504
ALGORITHMS
IRIS H.-R. JIANG
Administrative Matters
Introduction
2
¨ Time/location: 1CD3A@SC204
¨ Instructor: 㱆啀⥩ Iris Hui-Ru Jiang
¤ Email: huiru.jiang@gmail.com
¤ Office: ED540, ext. 31211
¤ Office hours: 1X (made by appointment)
¨ Teaching assistants: 愔⭰ⓙ㜵㉦䝦
¤ Email: nctuee.alg@gmail.com
¤ Lab: ED413, ext. 54226
¤ Office hours: 2EF
¨ Prerequisite: two out of the following courses
¤ Data structures
¤ Discrete mathematics
¤ Computer programming in C
¤ Computer programming in C++
IRIS H.-R. JIANG
Reading Materials
Introduction
3
¨ Course webpage:
¤ e3, NCTU open course ware
¨ Required text:
¤ Kleinberg and Tardos, Algorithm Design, Addison Wesley, 2006
n Jon Kleinberg, 20 Best Brains under 40, Discover Magazine,
2008
n Cornell
¨ Reference:
¤ S. Dasgupta, C. H. Papadimitriou, and U. V. Vazirani, Algorithms,
McGraw-Hill, 2007
n UC Berkeley
¤ Cormen, Leiserson, Rivest, Stein, Introduction to Algorithms, 3rd
Ed., McGraw Hill/MIT Press, 2009
n Bible! MIT
IRIS H.-R. JIANG
Course Objectives
Introduction
4
¨ Study unifying principles and concepts of algorithm design
¤ Algorithmic problems form the heart of computer science
¨ Polish your critical thinking and problem-solving technique
¤ Algorithmic problems tend to come bundled together with lots of
messy, application-specific detail, some of it essential, some of it
extraneous
¤ Two fundamental components
n Get to the mathematically clean core of a problem
n Identify the appropriate algorithm design techniques based on
the structure of the problem
¨ Intended audience:
¤ Who are interested in computer science
¤ Who are computing something
¤ Who are learning problem-solving techniques

4. Iris Hui-Ru Jiang Fall 2014
DEE3504
ALGORITHMS
IRIS H.-R. JIANG
Administrative Matters
Introduction
2
¨ Time/location: 1CD3A@SC204
¨ Instructor: 㱆啀⥩ Iris Hui-Ru Jiang
¤ Email: huiru.jiang@gmail.com
¤ Office: ED540, ext. 31211
¤ Office hours: 1X (made by appointment)
¨ Teaching assistants: 愔⭰ⓙ㜵㉦䝦
¤ Email: nctuee.alg@gmail.com
¤ Lab: ED413, ext. 54226
¤ Office hours: 2EF
¨ Prerequisite: two out of the following courses
¤ Data structures
¤ Discrete mathematics
¤ Computer programming in C
¤ Computer programming in C++
IRIS H.-R. JIANG
Reading Materials
Introduction
3
¨ Course webpage:
¤ e3, NCTU open course ware
¨ Required text:
¤ Kleinberg and Tardos, Algorithm Design, Addison Wesley, 2006
n Jon Kleinberg, 20 Best Brains under 40, Discover Magazine,
2008
n Cornell
¨ Reference:
¤ S. Dasgupta, C. H. Papadimitriou, and U. V. Vazirani, Algorithms,
McGraw-Hill, 2007
n UC Berkeley
¤ Cormen, Leiserson, Rivest, Stein, Introduction to Algorithms, 3rd
Ed., McGraw Hill/MIT Press, 2009
n Bible! MIT
IRIS H.-R. JIANG
Course Objectives
Introduction
4
¨ Study unifying principles and concepts of algorithm design
¤ Algorithmic problems form the heart of computer science
¨ Polish your critical thinking and problem-solving technique
¤ Algorithmic problems tend to come bundled together with lots of
messy, application-specific detail, some of it essential, some of it
extraneous
¤ Two fundamental components
n Get to the mathematically clean core of a problem
n Identify the appropriate algorithm design techniques based on
the structure of the problem
¨ Intended audience:
¤ Who are interested in computer science
¤ Who are computing something
¤ Who are learning problem-solving techniques

5. IRIS H.-R. JIANG
Course Content (1/3)
¨ Introduction
¤ An opening problem: stable marriages
¤ Range of problems we will consider
¨ Background:
¤ Basics of algorithm analysis
¤ Graphs
¨ General algorithmic techniques
¤ Greedy algorithms
n Finding optimal solutions with greedy methods
n Scheduling time intervals
n The minimum spanning tree problem
¤ The divide and conquer method
n Some basic primitives in computational geometry
Introduction
5
*The details are subject to change
IRIS H.-R. JIANG
Course Content (2/3)
¤ Dynamic programming with many applications
n Weighted interval scheduling
n Knapsack problems
n Shortest paths
n Sequence alignment
n Including efficient implementation via divide and conquer
¤ Flows and cuts in networks
n The basic flow and cut problems
n Basic methods: augmenting paths
n Application to matching
n Polynomial time methods
n Extensions to more general models
n Applications to resource allocation, sequencing, and
segmentation
Introduction
6
*The details are subject to change
IRIS H.-R. JIANG
Course Content (3/3)
¨ Computational Intractability (Optional)
¤ NP-completeness
n Hardness of problems in optimization and constraint
satisfaction
n How to show NP-completeness: reducibility
n Examples including the traveling salesman problem, 3-
dimensional matching, covering, packing, partitioning
problems, and subset sum
¤ PSPACE completeness
n Hardness of problems in artificial intelligence and game-
playing
Introduction
7
*The details are subject to change
IRIS H.-R. JIANG
Course Content (Optional)
¨ Algorithms for hard problems
¤ Improved exponential methods
¤ Approximation algorithms
n greedy algorithms (load balancing, facility location)
n The application of linear programming
¤ Local search techniques
n The Metropolis Algorithm
n Simulated annealing
n Applications to graph partitioning and neural networks
¨ Randomized algorithms
¤ Including contention-resolution protocols and satisfiability
heuristics
¨ Algorithms that run forever
Introduction
8
*The details are subject to change

6. IRIS H.-R. JIANG
Course Content (1/3)
¨ Introduction
¤ An opening problem: stable marriages
¤ Range of problems we will consider
¨ Background:
¤ Basics of algorithm analysis
¤ Graphs
¨ General algorithmic techniques
¤ Greedy algorithms
n Finding optimal solutions with greedy methods
n Scheduling time intervals
n The minimum spanning tree problem
¤ The divide and conquer method
n Some basic primitives in computational geometry
Introduction
5
*The details are subject to change
IRIS H.-R. JIANG
Course Content (2/3)
¤ Dynamic programming with many applications
n Weighted interval scheduling
n Knapsack problems
n Shortest paths
n Sequence alignment
n Including efficient implementation via divide and conquer
¤ Flows and cuts in networks
n The basic flow and cut problems
n Basic methods: augmenting paths
n Application to matching
n Polynomial time methods
n Extensions to more general models
n Applications to resource allocation, sequencing, and
segmentation
Introduction
6
*The details are subject to change
IRIS H.-R. JIANG
Course Content (3/3)
¨ Computational Intractability (Optional)
¤ NP-completeness
n Hardness of problems in optimization and constraint
satisfaction
n How to show NP-completeness: reducibility
n Examples including the traveling salesman problem, 3-
dimensional matching, covering, packing, partitioning
problems, and subset sum
¤ PSPACE completeness
n Hardness of problems in artificial intelligence and game-
playing
Introduction
7
*The details are subject to change
IRIS H.-R. JIANG
Course Content (Optional)
¨ Algorithms for hard problems
¤ Improved exponential methods
¤ Approximation algorithms
n greedy algorithms (load balancing, facility location)
n The application of linear programming
¤ Local search techniques
n The Metropolis Algorithm
n Simulated annealing
n Applications to graph partitioning and neural networks
¨ Randomized algorithms
¤ Including contention-resolution protocols and satisfiability
heuristics
¨ Algorithms that run forever
Introduction
8
*The details are subject to change

7. IRIS H.-R. JIANG
Course Content (1/3)
¨ Introduction
¤ An opening problem: stable marriages
¤ Range of problems we will consider
¨ Background:
¤ Basics of algorithm analysis
¤ Graphs
¨ General algorithmic techniques
¤ Greedy algorithms
n Finding optimal solutions with greedy methods
n Scheduling time intervals
n The minimum spanning tree problem
¤ The divide and conquer method
n Some basic primitives in computational geometry
Introduction
5
*The details are subject to change
IRIS H.-R. JIANG
Course Content (2/3)
¤ Dynamic programming with many applications
n Weighted interval scheduling
n Knapsack problems
n Shortest paths
n Sequence alignment
n Including efficient implementation via divide and conquer
¤ Flows and cuts in networks
n The basic flow and cut problems
n Basic methods: augmenting paths
n Application to matching
n Polynomial time methods
n Extensions to more general models
n Applications to resource allocation, sequencing, and
segmentation
Introduction
6
*The details are subject to change
IRIS H.-R. JIANG
Course Content (3/3)
¨ Computational Intractability (Optional)
¤ NP-completeness
n Hardness of problems in optimization and constraint
satisfaction
n How to show NP-completeness: reducibility
n Examples including the traveling salesman problem, 3-
dimensional matching, covering, packing, partitioning
problems, and subset sum
¤ PSPACE completeness
n Hardness of problems in artificial intelligence and game-
playing
Introduction
7
*The details are subject to change
IRIS H.-R. JIANG
Course Content (Optional)
¨ Algorithms for hard problems
¤ Improved exponential methods
¤ Approximation algorithms
n greedy algorithms (load balancing, facility location)
n The application of linear programming
¤ Local search techniques
n The Metropolis Algorithm
n Simulated annealing
n Applications to graph partitioning and neural networks
¨ Randomized algorithms
¤ Including contention-resolution protocols and satisfiability
heuristics
¨ Algorithms that run forever
Introduction
8
*The details are subject to change

8. IRIS H.-R. JIANG
Course Content (1/3)
¨ Introduction
¤ An opening problem: stable marriages
¤ Range of problems we will consider
¨ Background:
¤ Basics of algorithm analysis
¤ Graphs
¨ General algorithmic techniques
¤ Greedy algorithms
n Finding optimal solutions with greedy methods
n Scheduling time intervals
n The minimum spanning tree problem
¤ The divide and conquer method
n Some basic primitives in computational geometry
Introduction
5
*The details are subject to change
IRIS H.-R. JIANG
Course Content (2/3)
¤ Dynamic programming with many applications
n Weighted interval scheduling
n Knapsack problems
n Shortest paths
n Sequence alignment
n Including efficient implementation via divide and conquer
¤ Flows and cuts in networks
n The basic flow and cut problems
n Basic methods: augmenting paths
n Application to matching
n Polynomial time methods
n Extensions to more general models
n Applications to resource allocation, sequencing, and
segmentation
Introduction
6
*The details are subject to change
IRIS H.-R. JIANG
Course Content (3/3)
¨ Computational Intractability (Optional)
¤ NP-completeness
n Hardness of problems in optimization and constraint
satisfaction
n How to show NP-completeness: reducibility
n Examples including the traveling salesman problem, 3-
dimensional matching, covering, packing, partitioning
problems, and subset sum
¤ PSPACE completeness
n Hardness of problems in artificial intelligence and game-
playing
Introduction
7
*The details are subject to change
IRIS H.-R. JIANG
Course Content (Optional)
¨ Algorithms for hard problems
¤ Improved exponential methods
¤ Approximation algorithms
n greedy algorithms (load balancing, facility location)
n The application of linear programming
¤ Local search techniques
n The Metropolis Algorithm
n Simulated annealing
n Applications to graph partitioning and neural networks
¨ Randomized algorithms
¤ Including contention-resolution protocols and satisfiability
heuristics
¨ Algorithms that run forever
Introduction
8
*The details are subject to change

9. IRIS H.-R. JIANG
Grading Policy
Introduction
9
¨ Grading:
¤ Homework: 15%
¤ Programming: (two mini-projects: 10% + project: 25%)
¤ Exams: (Midterm: 25% + Final: 25%)
¨ Homework programming:
¤ Discussions are encouraged. However, solutions should be
written individually and separately (no credits for plagiarism)
¤ No late submission (partial solutions may get partial credits)
¤ Homework is usually due in two weeks
¤ Programming assignments are usually due in two or three weeks
¨ Exams
¤ No discussions, solutions should be written individually
IRIS H.-R. JIANG
What is an Algorithm?
Introduction
10
¨ Definition: An algorithm is
¤ A finite, definite, effective procedure, with some output
[Donald Knuth, 1968]
¤ Input: may have
¤ Output: must have
¤ Definiteness: must be clear and unambiguous
¤ Finiteness: terminate after a finite number of steps
¤ Effectiveness: must be basic and feasible with pencil and paper
¤ Procedure: the sequence of specific steps in a logical order
¨ Cf. An algorithm is
¤ A well-defined procedure for transforming some input to a desired
output [Cormen et al. Introduction to Algorithms, 2nd Ed.]
problem solution
Problem-solving
procedure

10. IRIS H.-R. JIANG
Grading Policy
Introduction
9
¨ Grading:
¤ Homework: 15%
¤ Programming: (two mini-projects: 10% + project: 25%)
¤ Exams: (Midterm: 25% + Final: 25%)
¨ Homework programming:
¤ Discussions are encouraged. However, solutions should be
written individually and separately (no credits for plagiarism)
¤ No late submission (partial solutions may get partial credits)
¤ Homework is usually due in two weeks
¤ Programming assignments are usually due in two or three weeks
¨ Exams
¤ No discussions, solutions should be written individually
IRIS H.-R. JIANG
What is an Algorithm?
Introduction
10
¨ Definition: An algorithm is
¤ A finite, definite, effective procedure, with some output
[Donald Knuth, 1968]
¤ Input: may have
¤ Output: must have
¤ Definiteness: must be clear and unambiguous
¤ Finiteness: terminate after a finite number of steps
¤ Effectiveness: must be basic and feasible with pencil and paper
¤ Procedure: the sequence of specific steps in a logical order
¨ Cf. An algorithm is
¤ A well-defined procedure for transforming some input to a desired
output [Cormen et al. Introduction to Algorithms, 2nd Ed.]
problem solution
Problem-solving
procedure